1.16.E35 (Q610)

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1.16.E35
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    Statements

    DLMF defining formula
    ⟨ ℱ ⁡ ( u ) , ϕ ⟩ = ⟨ u , ℱ ⁢ ( ϕ ) ⟩ , distribution distributional-Fourier-transform 𝑢 italic-ϕ distribution 𝑢 ℱ italic-ϕ {\displaystyle{\displaystyle\left\langle\mathscr{F}\left(u\right),\phi\right% \rangle=\left\langle u,\mathscr{F}(\phi)\right\rangle,}}
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    constraint
    ϕ ∈ 𝒯 n italic-ϕ subscript 𝒯 𝑛 {\displaystyle{\displaystyle\phi\in\mathcal{T}_{n}}}
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    Symbols used
    Q10879
    DLMF defining formula
    ⟨ Λ , ϕ ⟩ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}
    xml-id
    C1.S16.SS1.p5.m5amdec
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    Q10758
    DLMF defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2agdec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1qdec
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    space of test functions
    DLMF defining formula
    𝒯 𝒯 {\displaystyle{\displaystyle\mathcal{T}}}
    xml-id
    C1.S16.XMD12.m1dec
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    test function
    DLMF defining formula
    ϕ ⁢ ( x 1 , x 2 , … , x n ) italic-ϕ subscript 𝑥 1 subscript 𝑥 2 … subscript 𝑥 𝑛 {\displaystyle{\displaystyle\phi(x_{1},x_{2},\dots,x_{n})}}
    xml-id
    C1.S16.XMD13.m1fdec
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    Fourier transform of a test function (locally)
    DLMF defining formula
    ℱ ⁢ ( ϕ ) ℱ italic-ϕ {\displaystyle{\displaystyle\mathscr{F}(\phi)}}
    xml-id
    C1.S16.XMD15.m1cdec
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    Identifiers

     
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